Fireplace tiling question.

I'm am currently in the middle of finishing my basement.
We have installed a double sided fireplace in a wall that separates two rooms. The fireplace is 4' wide by 16" tall and sits 3' off the ground to the bottom of the fireplace.

On both sides, the tile will cover 6' horizontally, then floor to ceiling. The walls are about 10' long and flat...no mantels or boxing out.

My question is in regards to where the tile will end on the bottom and meet the floor. The floor will be done in a carpet, most likely berber.

Should the tile sit tight to the concrete floor, or leave a gap?

The concrete floor isn't completely level, so I'm thinking I might have to start a bit higher up with a board screwed into the wall for support, and then back fill the bottom tile the next day.